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Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.
1. Introduction
Understanding resonant interactions in nonlinear systems is a crucial step in understanding their global dynamic behaviour. A large class of resonant interactions may be described as a vibration-in-unison, meaning that the physical displacement coordinates of the system reach their extrema and pass through zero simultaneously. The vibration-in-unison concept was famously used by Rosenberg to give the first definition of a nonlinear normal mode for a conservative system [1–4]. In more recent work, the definition of nonlinear normal modes has been relaxed to include more general periodic motions (e.g. [5–9]). In this paper, we investigate the opposite case to that defined by Rosenberg, namely out-of-unison resonances, and demonstrate how they manifest themselves in systems of weakly nonlinear coupled oscillators.
Here we define out-of-unison resonance as a resonant interaction between two displacement coordinates of a conservative system, where one coordinate reaches an extrema as the other passes through zero, such that they are 90° out-of-phase. The best-known physical example of this behaviour is whirling which can occur, for example, in a taut cable [10]. As we shall show later, this type of resonance occurs when two underlying linear natural frequencies of the system are close, giving a resonance at a 1 : 1 frequency ratio.
Previous authors have applied approximate analytical techniques to problems involving weakly nonlinear oscillators (e.g. [11–15]). The phenomenon of internal resonance has also been analysed using similar approaches (for example [16] and references therein). An alternative method for studying internal resonance is to use nonlinear normal modes, as discussed in [7,17–22]. These techniques use an energy-based representation to show the free vibration responses of nonlinear systems.
In this paper, the second-order normal form technique [23] is used to analytically describe the dynamics of weakly nonlinear, conservative systems. These dynamical behaviours are equivalent to the nonlinear normal modes of the systems; however, they are represented in terms of displacement amplitudes rather than energy. As such, this technique is arguably better suited for practical applications. Furthermore, as this technique is applied directly to the second-order differential equations (the conventional formulation of many vibration problems), it lends itself to such problems more naturally than the classical first-order, state-space, equivalent [24–27]. A comparison between the first- and second-order normal form technique is given in [23], and further details on the second-order normal form technique can be found in [28–30].
A method for the application of the second-order normal form technique is introduced in §2. Then, in §3, we consider whirling motion in a taut, horizontal, undamped cable, which is a well-known physical example of out-of-unison resonance. In §4, we consider an in-line, conservative, two degree-of-freedom (2-d.f.) oscillator to demonstrate how out-of-unison motion may exist in other nonlinear systems. Furthermore, we demonstrate how, from the analytical descriptions developed, we may determine the values of the physical parameters that yield out-of-unison resonance. Finally, we demonstrate how the out-of-unison motion, seen in the conservative systems, translates to a similar behaviour when the in-line system is forced and damped (and so is non-conservative).
2. Second-order normal form technique
In this paper, we use the second-order normal form technique to transform the equations of motion of weakly nonlinear systems into sets of time-invariant equations, describing the approximate dynamics. The technique uses the assumption that the nonlinear terms are small; therefore, as the amplitude decreases the results converge to the true solution, but they diverge at higher amplitudes. Here, we consider responses in amplitude and frequency ranges where the nonlinear terms are small, and it is confirmed that the resulting errors are negligible via comparison with results found using numerical continuation. Methods for directly estimating the validity of the normal form results may also be used (e.g. [31]). The derivation and generalized application of the technique are given in [23,28], and the approach used here is also shown in [30]. For completeness, we now outline the key steps of the second-order normal form technique that are applied to the systems considered in this paper.
The equation of motion for a system with N d.f. may be written 2.1 where M, C and K are the {N×N} mass, damping and stiffness matrices respectively, Nx and Px are {N×1} vectors of nonlinear terms and forcing amplitudes, respectively, and Ωf is the forcing frequency. To find the backbone curves of this system, we consider the unforced and undamped equivalent of equation (2.1), which may be written as follows: 2.2 We now apply the linear modal transform x=Φq, where Φ is an {N×N} matrix whose nth column describes the modeshape of the nth linear mode, and q is an {N×1} vector of linear modal displacements. This allows equation (2.2) to be written as follows: 2.3 where Λ is an {N×N} diagonal vector where the nth leading diagonal element is the square of the nth natural frequency of the underlying linear system, , and Nq is an {N×1} vector of nonlinear terms.
Next we apply the nonlinear near-identity transform q=u+h(u), where u describes the fundamental response, and h (which is assumed to be small) contains the harmonic contents of q. From this, we can write the transformed equation of motion as 2.4 We assume un (the nth element of u and the fundamental response of qn) to be sinusoidal, such that it may be written 2.5 where Un, ωrn and ϕn are the amplitude, response frequency and the phase of un, respectively. Note that ωrn and ωnn are distinct and represent the fundamental response frequency and linear natural frequency of qn, respectively. The subscripts p and m denote the positive and negative (plus and minus) signs of the complex exponents, respectively.
As we are assuming the system to be weakly nonlinear, we assume that Nq is small in relation to other terms—denoted as order ɛ1, where ɛ is a bookkeeping parameter denoting smallness. Furthermore, as the harmonics are small we may also state that h is of order ɛ1. Therefore, we may write ɛNq(u+ɛh)≈ɛNq(u) whilst maintaining order ɛ1 accuracy. Substituting equation (2.5) into Nq(u) allows us to write Nq(u)=[nq]u* where [nq] is an {N×L} matrix of coefficients and u* is an {L×1} vector of all the unique combinations of unp and unm that exist in Nq(u). The ℓth element of u* can be written as follows: 2.6 where sℓkp and sℓkm are the exponents of ukp and ukm in , respectively.
Substituting equation (2.5) into equation (2.6) leads to 2.7 where and are the response frequency and phase of , respectively, and may be found using 2.8
We now define the {N×L} matrix β, where element {n, ℓ} of β is given by 2.9 Therefore, if the response frequency of , , is equal in magnitude to that of the nth linear mode, ωrn, then βn,ℓ=0. Hence any element in β with a value of zero corresponds to an element in [nq] describing the coefficient of a resonant term. We can now find the resonant nonlinear terms (see equation (2.4)) by defining Nu=[nu]u*, where [nu] is an {N×L} matrix of coefficients. As [nu] must be populated by the coefficients of resonant terms we use, for the {n,ℓ}th term 2.10a and 2.10b Although the calculation of h is not explicitly needed here, it may be found using h=[h]u* where hn,ℓ=nq,n,ℓ/βn,ℓ when βn,ℓ≠0, and hn,ℓ=0 when βn,ℓ=0 (see [23] for further details).
As all terms in the nth element of the vector Nu, written Nu,n, resonate at frequency ωrn, we may write 2.11 where and are complex conjugates. Substituting equations (2.5) and (2.11) into equation (2.4) allows us to write 2.12 From equation (2.12), we can see that the expressions in the square brackets are a complex conjugate pair. Therefore, as both of these expressions must equal zero, we may write the first expression as 2.13 This allows us to write N equations in the form of equation (2.13), which may be solved to find all Un and ϕn. In the cases considered here we assume the harmonics to be negligible and so we can write q=u, such that the linear modal transform may be written x=Φu.
3. An example cable system
Consider the dynamics of an unforced, undamped, horizontal cable under tension, as represented in figure 1. The dynamics of the cable can be described using the modal equations of motion derived by Warnitchai et al. [32], where the system is modelled using the sets of linear modes of the cable in the y- and z-directions. It is assumed that the motion in the x-direction is negligible. Owing to the influence of gravity (which acts in the z-direction), the cable exhibits a small sag, breaking the rotational symmetry about x. This leads to a difference in the dynamic behaviour of the corresponding linear modes in the y-direction and in the z-direction—most notably, a difference in the linear natural frequencies [14]. Here we consider the responses of the cable in the vicinity of the natural frequencies of the first linear modes in the y- and z-directions, whose displacements are written as q1 and q2, respectively. These two modes are used to describe the dynamics that are of particular interest.
An example of out-of-unison motion between coordinates can be seen in figure 2, which shows three whirling responses for the cable—labelled A, B and C. Figure 2a shows the projection of normalized time, t/T (where T is the period), against q1 and q2. Figure 2b shows the projection q1 against q2, the responses of the first linear modes in the horizontal and vertical directions, respectively, parametrized in time. As such, figure 2b is analogous to the path of motion of the cable in the y–z plane. It can clearly be seen that these coordinates are not vibrating in-unison. Instead, as one coordinate reaches an extrema, the other is passing through zero (although a slight deviation is seen, due to the sagging of the cable under gravity). As this system is conservative, this out-of-unison motion is not due to the influence of forcing or damping, but rather is a fundamental underlying behaviour of the system.
(a) Normal form decomposition
Using the normal form technique described in §2, we investigate the mechanisms behind the out-of-unison motion of the cable seen in figure 2. As the Warnitchai formulae describe the motion of the cable using modal coordinates, the equations of motion may be written in the form of equation (2.3) directly, where 3.1 where ωn1 and ωn2 (rad s−1) are the linear natural frequencies of the first linear modes in the y- and z-directions, respectively, and the nonlinear parameters are calculated using W=ν11/m and Q=β11/m. The parameter ν11 (kg m−2 s−2) arises from the stretching of the cable under deformation, β11 (kg m−1 s−2) describes the effect of the static sag and m (kg) is the mass of the cable. Details regarding how ωn1, ωn2, ν11 and β11 are calculated are given in [32].
Internally resonant responses require an integer ratio between the fundamental response frequencies, ωr1 and ωr2. As we are interested in internally resonant responses in the vicinity of the linear natural frequencies, which are close, we shall consider the case where Ω=ωr1=ωr2, where Ω denotes the common response frequency. Making the substitution qn=unp+unm into Nq (see equation (2.5)) we calculate [nq], u* and β as 3.2 where dashes in β represent elements whose values are of no significance as they correspond to elements in [nq] with a value of zero. Note that none of the nonlinear terms resulting from the effect of the static sag of the cable (described by Q) are resonant (i.e. correspond to a zero in β).
From equations (3.2), we may calculate [nu] (see equations (2.10)), and hence Nu, using Nu=[nu]u*. We may then calculate and (see equation (2.11)) as 3.3a and 3.3b Now, using equations (2.13) and (3.3), we may write 3.4a and 3.4b where we have used Ω=ωr1=ωr2. The real parts of equations (3.4) then lead to 3.5a and 3.5b where . The imaginary parts of equations (3.4) lead to for both equations. As a result, p=±1 where p=+1 corresponds to responses where u1 and u2 are in-phase or anti-phase, and p=−1 corresponds to u1 and u2 being ±90° out-of-phase.
Besides the trivial solution where U1=0 and U2=0, corresponding to no motion, two solutions to equations (3.5) can be found by setting U1≠0 and U2=0, and U1=0 and U2≠0. These correspond to sets of responses of the system, denoted S1 and S2, which are defined by 3.6 and 3.7 When both U1≠0 and U2≠0, equations (3.5) can be written as follows: 3.8 which may be rearranged to give 3.9 As ωn2≠ωn1 (due to the influence of gravity), p=+1 cannot be a valid solution.
For the case where p=−1 two additional sets of responses, denoted S3+ and S3− (or S3± when referring to both), are produced. S3± have the phase differences (ϕ1−ϕ2)=±π/2. Substituting p=−1 into equation (3.9) and rearranging gives the amplitude relationship 3.10a and substituting this into equation (3.8) gives the response frequency relationship 3.10b Owing to the ±π/2 phase differences, the responses represented by S3± are out-of-unison resonances between q1 and q2. Physically, these are representative of a whirling in the first linear modes of the cable, where the two solutions represent clockwise and anticlockwise motions. The identical amplitude and frequency relationships for S3+ and S3− illustrates that the behaviour of the cable is unaffected by the direction of motion. As the S3± branches meet S1 (where U2=0) at a bifurcation, the point on S3± where U2=0 is the point at which the bifurcation occurs. From equations (3.10), this point is described by 3.11 which is also a point on S1, which can be seen from equation (3.6). These results define the response in u. For the full response, the transform q=u+h may be used, in which h contains the harmonic contents of the response. Here we assume that h is negligible.
(b) Example of a cable system
We now consider a cable with a length of 1.5 m, a diameter of 5 mm, a density of 3000 kg m−3, a Young's Modulus of 2×1011 Pa and a static tension of 200 N. The equations derived by Warnitchai et al. [32] lead to a system with linear natural frequencies ωn1=122.04 rad s−1 and ωn2=123.87 rad s−1, and nonlinear coefficient W=3.2×108 m−2 s−2. The nonlinear coefficient Q (see equation (3.1)) is not needed as we do not consider any harmonic components.
The responses of this cable, calculated using the numerical continuation software AUTO-07p [33], are shown in figure 3. This figure shows the projection of the common response frequency, Ω, against the absolute displacement amplitude , where Q1 and Q2 are the maximum amplitudes of q1 and q2, respectively. In the region shown here, the maximum error in , between the results of the continuation and the second-order normal form technique, is less than 3%. The predicted position of the bifurcation point (see equation (3.11)) is slightly different to the numerically computed position in both Ω and . A metric based on the Euclidean norm of the errors in Ω and gives an error of 3.2%. These small errors validate both the accuracy of the results of the technique and the assumption that the harmonics are negligible (as the numerically computed results contain harmonics). These numerical results also determine the stability of the responses, although the stability of solutions may also be found analytically [30,34].
Three embedded plots in figure 3 illustrate the responses of the cable in the linear modal coordinates in the projection q1 against q2. The embedded plot showing out-of-unison motion is illustrative of responses on S3+ and S3− for clockwise and anticlockwise motion, respectively (represented by opposing arrows labelled '+' and '−', respectively). As with figure 2b, the responses shown in the embedded plots are analogous to the paths of motion of the cable in the y–z plane. Three points labelled A, B and C on the S3+ branch correspond to the three responses depicted in figure 2. From figure 2a it can be seen that, in the projection shown in figure 2b, the cable is whirling in a clockwise direction. If the corresponding responses on S3− were shown, the motion would be anticlockwise.
Although it is not shown here, the responses in S1 contain a small component of q2 responding at twice the frequency of q1—representative of a swaying motion of the cable. As this is small (Q2<0.01Q1 in the stable region) it does not violate the assumptions made in the normal form analysis and would be predicted as a harmonic response. The bifurcation on S1 shows the point at which the horizontal swaying motion loses stability and becomes a stable whirling motion (on S3±). This is a supercritical pitchfork bifurcation, with S1 losing stability and two stable branches, S3±, emerging. Owing to the projection used in figure 3, the S3+ and S3− branches are superposed, as the amplitude of the whirling is unaffected by the direction of motion.
In this section, it has been shown, using the second-order normal form technique, that the whirling of a cable is an out-of-unison resonant response. In the next section, we show that out-of-unison resonance may also exist in in-line systems.
4. An in-line oscillator
We now consider an in-line, symmetric, 2-d.f. oscillator with forcing and damping (although we focus initially on the undamped case). This differs from the cable system considered in §3 insofar as it is non-conservative and the coordinates share the same physical dimension, x. To understand the underlying dynamics of this system, we consider its backbone curves. These describe the loci of responses of the unforced, undamped equivalent system, and they relate to the responses of the system when forced and damped.
This system, shown in figure 4, is similar to that considered in [30]; however, here we consider a more general case where the springs may be hardening or softening, leading to additional solutions. Two lumped masses, both of mass m, have displacements x1 and x2 and are each forced sinusoidally at amplitudes P1 and P2, respectively, and at frequency Ωf. They are connected to ground via linear viscous dampers, damping constant c, and via nonlinear springs with the force–deflection relationship F=k(Δx)+κ(Δx)3. The masses are also connected via a linear viscous damper, constant c2, and a nonlinear spring with the force–deflection relationship F=k2(Δx)+κ2(Δx)3.
(a) Backbone curves
The equations of motion of the forced and damped system shown in figure 4 can be written in the form of equation (2.1). However, as we are interested in the backbone curves of this system, we may describe the motion directly in the form of equation (2.2), with 4.1 where κ and κ2 may be positive or negative. We may now apply the linear modal transform, x=Φq, to equation (4.1) such that it may be written in the form of equation (2.3), where 4.2 where γ=1+8κ2/κ, and ωn1 and ωn2 are the first and second linear natural frequencies, respectively. These are calculated as and . Here we assume that ωn1 and ωn2 are close, such that the fundamental components of q1 and q2 respond at the same frequency. We also assume that, when the system is forced near resonance, the fundamental components of q1 and q2 will respond at the forcing frequency Ωf. Hence, for convenience, we define the common response frequency as Ω, i.e. Ω=Ωf=ωr1=ωr2 where, as in §3, ωrn is the fundamental response frequency of qn for n=1,2. We now make the substitution qn=un=unp+unm into Nq, from which we calculate [nq], u* and β as 4.3 where elements in β containing a dash correspond to zero-valued elements in [nq].
We may now calculate [nu] using equations (2.10) and (4.3). The relationship Nu=[nu]u* may then be used to find and (see equation (2.11)) as 4.4a and 4.4b Now, using equations (2.13) and (4.4), we may write 4.5a and 4.5b The two solutions in which u1 and u2 are independently non-zero are labelled S1 and S2, respectively 4.6 and 4.7 When u1 and u2 are both non-zero, equations (4.5) may be written as follows: 4.8 where, as equation (4.8) must be real, the phase difference is given by 4.9 such that p=+1 corresponds to (i.e. u1 and u2 are in-phase or anti-phase), and p=−1 corresponds to (i.e. u1 and u2 are ±90° out-of-phase). Setting p=+1 yields two backbone curves, labelled S3+ and S3−, with the phase differences 4.10 Substituting p=+1 into equation (4.8) leads to the amplitude and response frequency relationships 4.11a and 4.11b The case where p=−1 yields a further two backbone curves denoted S4+ and S4−. These are characterized by the phase differences 4.12 Substituting p=−1 into equation (4.8) gives the amplitude and response frequency relationships 4.13a and 4.13b From the phase relationships given in equation (4.12), it can be seen that, for this system, responses on the S4± branches are out-of-unison.
As an example, we now briefly consider the system described in [30], in which the springs are hardening. Figure 5 shows the backbone curves S1, S2 and S3± for this system, in the projection of the common response frequency, Ω, against the maximum amplitude of displacement of the first physical coordinate, X1. As in the previous example, these results were calculated using numerical continuation and are in good agreement with the results of the second-order normal form technique. The maximum error between these methods in X1 is less than 1% and the error in the position of the bifurcation point, measured as the Euclidean norm of the errors in Ω and X1, is less than 0.03%. Four embedded plots illustrate the responses on the backbone curves in the projection q1 against q2, parametrized in time. Equations (4.11) show that S3± are composed of both q1 and q2, giving asymmetric responses in x1 and x2. This asymmetry is such that figure 5 would appear to be identical if shown in the projection Ω against X2 (rather than X1), except that S3+ and S3− would be interchanged. For further details, see [30].
For this system, with these parameters, out-of-unison responses are not seen (i.e. there are no valid solutions for S4±). To investigate why S4± do not exist here, we now consider how the nonlinear parameters, κ and κ2, affect the existence of the backbone curves.
(b) Effects of nonlinear parameters on the existence of backbone curves
We now investigate the ranges of values of the nonlinear parameters, κ and κ2, for which the backbone curves S3± and S4± may exist. This is done by firstly finding the parameter values that yield valid solutions to the bifurcations onto S3± and S4±, as a valid bifurcation must lead to a valid backbone curve. We then investigate whether the backbone curves may exist without a bifurcation, i.e. whether the ranges that yield non-physically valid bifurcations may lead to physically valid S3± and S4± solutions. We define a valid solution as one in which the common response frequency, Ω, and amplitudes, Un, are real and positive. We assume that m>0 and ωn2>ωn1.
Equation (4.13a) shows that U2=0 cannot be a solution on S4±. Therefore, S4± cannot meet S1 at any point. Using equations (4.13), the point at which U1=0 on S4± is given by 4.14a and 4.14b Equation (4.7) shows that this is a solution for S2, and hence represents the position of the bifurcation from S2 onto S4±. Using equations (4.14), and recalling that γ=1+8κ2/κ, we find the relationships 4.15a and 4.15b which must be satisfied for the existence of valid solutions of the bifurcation onto S4±. It may be possible for valid solutions to exist that originate from a non-real bifurcation point. To investigate this, from equations (4.15), the regions in which the bifurcation onto S4± does not exist are given by 4.16a and 4.16b Using equation (4.13a), it can be seen that κ2>0 cannot lead to any valid S4± solution, regardless of the value of κ. Thus, the region defined by equation (4.16a) cannot yield an S4± solution. To investigate the region given by equation (4.16b), we consider equation (4.13b) which, after eliminating U2 using equation (4.13a), may be written as follows: 4.17 When equation (4.16b) is true, the expression within the square brackets in equation (4.17) is negative. As we have also determined that κ2<0 is required for a valid solution, the expression within the braces must be negative. As κ<0 (a condition given by equation (4.16b)), the final term in equation (4.17) is also negative, hence the right-hand side of the equation is negative and no valid solution exists. Therefore, equations (4.15) describe the only regions in which solutions to S4± may exist.
Using this approach, the position of the bifurcations onto S3± can also be found and the existence of S3± may be determined. This reveals that S3± can emerge from both S1 and S2, and that no valid solution for S3± exists when a valid bifurcation does not exist. The regions in which valid solutions for S3± and S4± exist are summarized in figure 6. The hatched-green and hatched-red areas show where bifurcations exist on S1 and S2, respectively. Thick-blue lines represent the boundaries of the regions. A blue circle and a blue dot represent the positions of the systems used in figure 5 and in figure 7, respectively. In figure 6a, the area cross-hatched with both green and red represents the region in which the S3± backbone curves meet both S1 and S2. In figure 6b, it can be seen that the blue circle is outside any valid region, which is representative of no valid solutions to S4± existing for the parameter values used in figure 5.
(c) Out-of-unison motion in an in-line system
Figure 7 shows the backbone curves for a system where m=1, ωn1=1, ωn2=1.005, κ=−0.25 and κ2=−0.05. These are shown in the projection of the common response frequency, Ω, against the maximum amplitude of displacement of the first linear modal coordinate (Q1) in 7a, the second linear modal coordinate (Q2) in 7b and the first physical coordinate (X1) in 7c.
As illustrated by the blue dots in figure 6, backbone curves S3± and S4± all exist and bifurcate from S1 and S2, respectively. As with the example in figure 5, these are symmetry-breaking pitchfork bifurcations. The results shown here were calculated using numerical continuation and show good agreement with the predictions of the second-order normal form technique (not shown); specifically, the maximum error in X1 is less than 1%. The Euclidean norm of the error in Ω and X1 of the bifurcation positions is less than 0.001% for the bifurcation from S1 onto S3± and less than 0.002% for the bifurcation from S2 onto S4±.
The bifurcation from S1 onto S3± is indicated with a blue dot labelled 'BP1'. It can be seen in figure 7a,b that this causes a loss of stability of the S1 branch for responses at amplitudes above this bifurcation. These also show that S3± contain contributions from both q1 and q2, indicating an internal resonance between the two linear modal coordinates. Figure 7c shows S3− reaching an amplitude of zero in the physical coordinate X1 at a particular response frequency Ω. As q1 and q2 are in anti-phase (see equation (4.10)) and x1=q1+q2 (see equation (4.2)) this is representative of the point at which Q1=Q2. From equations (4.11), it can be seen that, neglecting harmonics, this point occurs when .
The bifurcation from S2 onto S4± is represented with a blue dot labelled 'BP2'. In all projections shown here, S4+ and S4− are superposed. This is because, neglecting harmonics, the linear modal displacement amplitudes are identical in S4+ and S4− (see equations (4.13)) and the phase differences, ±π/2, lead to identical displacement amplitudes in the physical coordinates. It can be seen in figure 7b that Q2 is constant on S4±, as predicted in equation (4.13a). As in the previous example, figure 7c would appear to be identical if shown in the projection Ω against X2, except that S3+ and S3− would be interchanged (while S4+ and S4− would remain superposed).
As the S4± branches are stable, we see that the conservative in-line system represented by the backbone curves exhibits a set of stable responses, where the underlying linear modal coordinates are ±90° out-of-phase. This motion is similar to the whirling seen in the cables except that, in this system, the linear modal coordinates share the same spatial dimension. This demonstrates that two coordinates may resonate out-of-unison in an in-line system.
An out-of-unison response in the linear modal coordinates (q1 and q2) corresponds to a set of responses in the physical coordinates (x1 and x2) that are nearly out-of-unison. To find the point at which the physical coordinates are precisely out-of-unison, we use equation (4.2) such that (neglecting harmonics) we may write x1 and x2 as 4.18a and 4.18b When ϕ1−ϕ2=±π/2, equations (4.18) may be written as follows: 4.19a and 4.19b Letting and , equations (4.19) can then be written 4.20a and 4.20b We may also write 4.21 When the phase difference between x1 and x2 is ±π/2 then, from equations (4.20), ψ=π/4. Substituting this into equation (4.21) leads to U1=U2. Hence, for responses on the S4± branches (where the underlying linear modal coordinates are out-of-unison), if the amplitudes of the two linear modal coordinates are equal, the physical coordinates, x1 and x2, are also vibrating out-of-unison.
(d) Forced response of an example system
We now compare the backbone curves to the forced and damped responses of this system. The damping and forcing parameters used here are c=0.002, c2=5×10−6 and [P1,P2]=[0.0015,−0.0015]. All other system parameters are those used in §4c. Owing to the antisymmetric shape of the forcing, only the second underlying linear mode, q2, experiences direct modal forcing. We therefore expect the forced responses to only follow backbone curves with a q2 component (i.e. the responses will not follow S1). Figure 8 shows the backbone curves of this system (as presented in figure 7) compared with the forced responses. This is shown in the projection of the common response frequency, Ω (assumed to be equal to the forcing frequency, Ωf), against the maximum displacement amplitude of the first physical coordinate, X1. Light-blue lines represent S1, S2 and S3± whilst dark-blue lines represent S4± (which are superposed, as described in §4c). Thin-black and dashed-red lines show the stable and unstable forced responses, respectively. The forced responses that are of interest here (following S4±) are highlighted with a thick-black line. Other responses in figure 8 are beyond the scope of this study.
As the excitation is in the shape of the second linear mode, there exists a typical Duffing-like softening response that envelops the backbone curve S2. This branch of the forced response (shown in figure 8) is referred to as the primary branch and, as with S2, is composed only of a response in q2. Near the frequency Ω=0.995, there is a bifurcation from this primary branch onto two secondary branches that follow S4±. These branches are internally resonant responses as q1 is present, but not directly forced. For amplitudes above this bifurcation, the primary branch becomes unstable. This is clearly analogous to the responses of the backbone curves, where S2 loses stability at amplitudes above the bifurcation onto S4±. At the points labelled D1,2 in figure 8, the secondary branches reach fold bifurcations and begin to follow S3±. As with the backbone curves, the symmetry of the system allows the physical coordinates to follow either of the secondary branches of the forced responses.
Four sets of points—labelled A1,2, B1,2, C1,2 and D1,2—represent four forced responses, where the subscripts 1 and 2 denote the responses in the coordinates x1 and x2, respectively. These responses, parametrized in time, are shown in figure 9, where figure 9a,b shows the responses in the linear modal coordinates, q1 against q2, and figure 9c,d shows the responses in the physical coordinates, x1 against x2. Response A1,2, on the primary forced branch, is shown in figure 9a,c and is clearly only composed of q2, which is represented in the physical coordinates by an oscillation in anti-phase. Responses are situated on the secondary forced branch. Owing to the symmetry-breaking bifurcation, we can determine that this branch is tending towards the S4− backbone curve. Responses are represented in figure 9b,d and clearly demonstrate out-of-unison motion in the modal coordinates. A slight distortion, owing to the influence of the forcing and damping, is seen in the out-of-unison responses and the degree of distortion increases as the responses diverge from S4− (i.e. the distortion in D1,2 is greater than in B1,2). Reducing the forcing and damping would result in the secondary branches collapsing onto S4− and a decrease in the distortion of the responses.
Figure 9b shows that, aside from the distortion, the linear modal coordinates are out-of-unison for responses on the secondary branches, i.e. as one coordinate reaches an extrema the other passes through zero. Figure 9d shows that, in responses B1,2 and D1,2, the physical coordinates are neither in-unison nor out-of-unison, i.e. as one coordinate reaches an extrema or zero the other does not. In response C1,2, however, the physical coordinates are out-of-unison (aside from the distortion). As discussed in §4c, this corresponds to the point on the backbone curves where the amplitudes of q1 and q2 are equal (neglecting harmonics). The similarity between the corresponding responses in the forced system and in the backbone curves shows that, for lightly damped systems, the forced response is governed by the backbone curves.
5. Conclusion
In this paper, we have investigated the phenomenon of out-of-unison resonance for systems of weakly nonlinear, coupled oscillators. This phenomenon has physical manifestations, such as whirling in a taut cable, and we have shown how this phenomenon can be modelled in order to describe the dynamic behaviour of the system. A cable was modelled using two sets of modes, one in the vertical and the other in the transverse direction, where the natural frequencies of the corresponding modes are close. The proximity of these natural frequencies allows for resonant interactions between the modes at a 1 : 1 ratio and leading to out-of-unison resonance. We then investigated an in-line nonlinear oscillator, with two close linear natural frequencies. Using a backbone curve analysis, we demonstrated that there were specific parameters for this system that led to out-of-unison resonance. In addition to this, we considered the case where the system was forced and lightly damped using continuation methods to track the steady-state periodic motion. As would be expected for a lightly damped system, the forced responses were shown to be governed by the backbone curves defined for the underlying conservative system. Therefore, for this particular system, we were able to show examples of resonances in the forced responses that have similar features to those obtained from studying the underlying conservative system.
Funding statement
The authors would like to acknowledge the support of the Engineering and Physical Sciences Research Council. T.L.H. is supported by an EPSRC studentship and S.A.N. is supported by EPSRC Fellowship EP/K005375/1. A.C. and D.J.W. are supported by EPSRC grant EP/K003836/1.
- Received September 1, 2014.
- Accepted October 17, 2014.
© 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.


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1998 Aluminum Featherlite 2 Horse straight load with custom tack area in excellent shape. You can pull it with an SUV or 1500 truck. It is 7'6" tall and…$7,000
4 horse slant load, padded dividers, rear tack, Large living quarters, 100" long wall, 91" shorter wall and 54" wall with door. Pulls excellent!$11,500
2002, Exiss 4 horse slant load with tack room, storage, side steps to windows, stallion dividers, water tank with faucet to outside and hose, tie rings…$12,000
Exiss 4 Horse Stock design trailer. Sierra Interior includes Propane stove, stainless steel sink, shower and toilet, A/C, TV, Antenna, Mount, Rear View…$43,000
I'm selling a 2006 Logan Coach Contender 3 horse slant steel gooseneck trailer. The trailer is in excellent condition and has been recently serviced and…$7,500
This trailer has barley been used for its model year. Just had the entire living space remodeled with new wood floors, shelving, little closet space, and…$8,300
This trailer is in great shape, super low miles, tires, brakes, and bearings all in great shape. Steel frame with aluminium, Dressing room with saddle…$7,500
4-Star 4 horse stock/combo with warmblood size stalls, lined & insulated roof in horse compartment, rear easy lift ramp behind full width stock door, removable…$30,000
Lovingly kept top of the line Brenderup with multiple upgrades -- saddle pole racks replaced with broad saddle racks, door hold-backs installed, back up…$6,000
A little exterior rust, but is a solid dependable quiet horse trailer. Priced to sell!$3,000

subset: commoncrawl


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"A World of Magic at Your Door!"
Per Adult From
$610ex, Land Only
$610ex, Land Only
$610ex, Land Only
Price Inclusions
* Return airport transfers
* 4 nights in a Deluxe Room, twin share
* Hot buffet breakfast daily
* Anaheim Dine for Less Card offering discounts up to 25% off food for 4 people per card at selected restaurants
* Free Wifi
* Free parking for one car only
* Free use of business centre and gym
Prices shown are a guide only, based on low season availability & some conditions. Please contact one of our Holiday Champions for an exact quote on the dates you wish to travel & any conditions that may apply
Desert Palms Hotel and Suites At a Glance
Located in America's Anaheim Region
- 1 block from theme parks
- Daily hot breakfast included
- Complimentary WiFi
Full Service Resort
Need more info? Visit the Desert Palms Hotel and Suites resort page.
Welcome to a fantastic family hotel in Anaheim. Located less than a block from the Disneyland, it is the ideal hotel to base the family during your stay. Enjoy a complimentary breakfast each morning with a great variety, before hitting the parks. If you want a break in the day, come back and enjoy the pool or chilling out. The kids will have a fantastic time here too - they can have their own registration or play the games in the lobby area.


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The very first book that I read in 2018 was Outcasts United by Warren St John, a non-fiction book that tells the story of a group of refugees from various countries around the world, trying to settle into a new life in small-town America, helped along by their relentless and passionate Jordanian soccer coach, Luma Mufleh. (Click through to read my review.)
While many of the mothers in the story are out working one or multiple jobs to try and get their new life on track, the kids are often left to keep house and feed the rest of the family, so there were several mentions of traditional foods from the various countries that they come from. This one immediately caught my eye.
p135 Kanue's role was to cook and keep the apartment. After classes each day at a public school called Avondale Middle, he went home and got to work making African food from recipes he'd learned from Grandma : beans and spicy stews of spinach and cassava leaves, which he poured over rice, and his favourite, peanut butter soup.
The idea of putting peanut butter into a soup sounded very strange to me, and I had visions of something very gloopy, oily and cloying. However, after googling it, I discovered that it is the national dish of Ghana, so surely a whole nation can't be wrong ! There are several versions available, many involving chicken, some as vegetarian options, with butternut squash, sweet potato or spinach. My original plan was to use up the leftover chicken after the Sunday roast, but we ended up eating raclette instead (a French dish consisting of potatoes, cured meats and oodles of melted cheese), so I went for a veggie version instead. I was actually pleasantly surprised by the end result.
Peanut Butter Soup
ingredients :
drizzle of olive oil
1 onion
1 clove of garlic
1 sweet potato
spinach, fresh or frozen
(optional : chicken, cooked or raw)
1 chicken stock cube
1 tin of chopped tomatoes
2 heaped tbsp peanut butter
salt, pepper, chilli flakes
ground peanuts (to serve - optional)
Start by peeling and dicing the sweet potato into small cubes.
Fry the onions and garlic in the olive oil until they start to go translucent and soft, but don't go brown. If using fresh chicken, you could add it at this point.
Add the sweet potato to the pot and cook for five minutes or so, stirring regularly.
Cover with boiling water and stir in the stock cube.
Cook for about 10 minutes until the sweet potato is soft but not mushy.
Add some spinach to the pot - I used frozen as I had some that needed using up, but fresh would be good too, or you can substitute for kale. Another common ingredient in American versions is Collard Greens and I'm sure they have an alternative green vegetable in Ghana/Africa so just use whatever you have to hand.
Stir through a tin of chopped tomatoes and heat through until the spinach is wilted and, if using frozen, completely defrosted. If using up leftover cooked chicken, add it now.
OK, here goes - time to dollop in the peanut butter. I had smooth but you could opt for crunchy instead if you prefer.
Cook over a low heat, stirring constantly, for a few minutes until the peanut butter has melted and gone creamy. Taste and season with salt, pepper and chilli flakes.
I had a bag of ground peanuts in the cupboard so I sprinkled some on top of each bowl after serving.
It's a rich, creamy and surprisingly tasty soup, and all the different flavours blend and work together really well. The Madhouse kids were intrigued and wanted to try it, despite not being at all keen on spinach and sweet potatoes. Bonus !
Adding to the #readcookeat linky over at Chez Maximka.
Also adding to the #KitchenClearout linky as it used up some frozen spinach that had been lurking in the freezer for ages, along with a jar of peanut butter that had all the oil separating from it and the end of a bag of ground peanuts.
Linking up to the brand new World Food Linky over at Jess Eats and Travels
Linking up to the brand new World Food Linky over at Jess Eats and Travels


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Today's Healthcare System Is More Challenging Than Ever
This typically means less personal attention from your healthcare providers. As for medication, it can result in higher prescription costs, unrecognized drug interactions, side effects, or worse. That is, until now.
Your Personal Medication Consultant
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If you are taking more than one prescription medication, or you have prescriptions from more than one doctor, you run a higher risk of having issues with your medication therapy. We are experts and specialize in medications. We can help assess your situation to make sure you are taking the right medications, at the right time, in the right doses, for the proper duration of therapy.
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Healthcare costs continue to rise and the incentives reside in ensuring that effective and appropriate use of healthcare is maintained and internal (and externally mandated) goals are reached. We work with acute care facilities, IPAs, insurance companies and employers to enact solutions to boost cost-effectiveness of medication use and safety, focusing on transitions of care, medication reconciliation, chronic disease management, medication compliance, and utilization.


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Words containing goingl
Found 5 words containing goingl. Browse our Scrabble Word Finder, Words With Friends cheat dictionary, and WordHub word solver to find words that contain goingl. Or use our Unscramble word solver to find your best possible play!
- Scrabble
- Words With Friends
- WordHub
- Crossword


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Fiona AppleSinger-songwriter, musician, record producer, pianist
- Video
Fiona Apple is an American singer-songwriter whose debut album "Tidal" earned her a Grammy Award for Best Female Rock Vocal. It was written when she was seventeen. A year later in 1997, she released the second works "Sleep to Dream" and in 2000 was"Fast As You Can". They both were nominated by The Best Clip Of The Year. Additionally, Fiona is a pianist and record producer as well.
Before fame
She was born to Diane McAfee, who is a singer and Brandon Maggart, who is an actor. Fiona Apple was trained to play piano as she was a child. At the age of 12, she was raped when living with her mother nad sister, which inspired her to write "Tidal".
Related to
Fiona Apple appeared at a number of performances by
Blake Mills, who is an American songwriter, guitarist, producer in 2014.


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Online Activism: #EpicFail?Submitted by Darsha Indrajith on Mon, 04/28/2014 - 20:38.
Have you liked the "Save Darfur" Facebook cause? If you have, you're probably a slacktivist. Science says so.
Before we rave about new SABC channelSubmitted by tyson on Mon, 07/29/2013 - 20:59.
So the SABC is set to launch its first ever 24-hour news channel by 1 August. Great stuff. A small step for news coverage and a giant leap for the public broadcaster. But before we get carried away, let's not forget one thing. Or two. In fact there's quite a lengthy to-do list.
Trust media truthSubmitted by nmlstudent on Sun, 05/20/2012 - 13:34.
by Isabelle Abraham
As more phone-hacking incidents come to light, the UK media is bearing the brunt of the mounting number of lawsuits. News24 reported that as of 20 April, the cases brought against News of the World has now amounted to a staggering 100. Another UK organisation, British broadcaster Sky News, has admitted to hacking emails, but justifies this decision as 'public interest'. Sky News is a part of BSkyB – of which 39% is owned by Rupert Murdoch's News Corporation.
Why telecoms operators will trump digital broadcastersSubmitted by Guy Berger on Sun, 11/28/2010 - 01:59.
November's launch of DStv mobile via DVB-H broadcasting symbolises a lot more than you being able to receive TV channels on your cellphone.
The move complements the existing DStv mobile offerings via 3G, available on Vodacom.
The difference is that users pull the content on the 3G service, whereas the new DVB-H is continuously pushed across the airwaves – i.e. the signals are broadcast.


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Recruitment Notification Highlights
- 1 Ford Off Campus 2018
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- 1.2 Ford Off Campus 2018 Required Skills
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- 1.4 Ford Off Campus Drive 2018 Eligibility Criteria
- 1.5 Ford Off Campus Drive 2018 Salary Details
- 1.6 Ford Off Campus Drive 2018 Selection Procedure
- 1.7 Ford Off Campus 2018 Registration Process
- 1.8 Ford Off Campus 2018 – Mandatory Certificates Need To Carry
- 1.9 How To Apply For Ford Off Campus 2018
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Ford Off Campus 2018
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Ford Off Campus 2018 Drive Details
|Organization Name
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|Freshers and Experienced
|Graduate or Post Graduate
|Work Location
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International Internet Magazine. Baltic States news & analytics
Friday, 17.08.2018, 11:51
Inflation behind rise in people living below poverty line in Lithuania – expert13.08.2018
Inflation and related growth in living standards were behind a rise in people living below the at-risk-of-poverty threshold in Lithuania last year, informs LETA/BNS referring to the economist Gitanas Nauseda, an adviser to the SEB bank's president.
Keyword tags: Analytics, Inflation, Lithuania, Quality of life, Statistics
Lithuanians are least saving among EU countries07.08.2018
Lithuanian residents are least saving among EU member states, and the Bank of Lithuania says people's trust in the economy has to do with it.
Household consumption expenditure in Lithuania increased by one-fifth26.06.2017
Statistics Lithuania informs that based on the provisional data of the Household Budget Survey, in 2016, average household consumption expenditure equalled EUR 298 per capita per month. Compared to 20121, monthly consumption expenditure grew by 20.3%, or EUR 50. Consumer price growth adjusted, compared to 2012, consumption increased by 18.9%.
Cost of living in Riga is 126th highest in the world21.06.2017
Riga has been ranked the world's 126th most expensive location and the cost of living in the Latvian capital is significantly higher than in the other two Baltic capitals – Tallinn and Vilnius, a survey by Mercer Human Research Consulting shows.
African, Asian, and European cities dominate the list of most expensive locations for working abroad21.06.2017
In a rapidly changing world, mobility has become a core component of multinational organizations' global talent strategy. To support the growing number of international assignees working in an increased number of locations, organizations are focusing on evaluating assignments from a cultural perspective, preparing for regional and lateral moves, and modifying compensation approaches to stay competitive. As organizations grapple with these challenges, they are working hard to accommodate the needs of their workforce and to support employees' careers. According to Mercer's 2017 Global Talent Trends Study, fair and competitive pay as well as opportunities for promotion are top priorities for employees this year – not surprising given the current climate of uncertainty and change.
Official statistics: 50,000 emigrated from Lithuania in 2016 and 14,000 this year
Over 50,000 people emigrated from Lithuania last year, in addition to nearly 14,000 in the first two months of 2017, according to the official statistics writes LETA/BNS.
Best Countries for Women Working Abroad
An above-average share of women worry about the cost of living and taxation abroad before their move and more than one-third actually end up earning less than at home (36%). But money is not everything: six in ten are satisfied with their occupation, work-life balance, and financial situation abroad. Nearly 80% of expat women consider themselves happy with their life and three in ten are even thinking about staying abroad forever (31%).


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1964 The Beatles announce changes to.. Tote Bag
1964 The Beatles announce changes to their Kansas city concert on their first tour of the USA
More Product Info »
More Details
• Shipping: Usually ships within 2-3 day(s)
• Media: 100% Cotton
• Capacity: 10 Litres
• Dimensions: 42 x 38cm
• Image Size: 20 x 28cm (approx)
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This is an automated preview only. Actual design may vary. All products are hand finished by our expert manufacturers and the best crop available will always be selected


text:
It's now even cheaper to order at the Alfa Matrix webstore, check out our new shipping costs conditions!
Choose your FREE "Sounds From The Matrix" CD compilation during checkout!
Bank / Money Transfer + Paypal
For the occasion of a special Alfa Matrix event at the B52 music club in Eernegem (Belgium) in November 2016 which gathered three Belgian acts from the label, PSY'AVIAH, MILDREDA and LLUMEN, an exclusive split-album compilation was offered to all event visitors. 100 more copies have been manufactured for the hardcore followers of the label and of these new Belgian EBM generation ambassadors, who could not make it that night to the concert.
This 9-track EP features the exclusive result of a remix war organized by the 3 bands plus 3 bonus songs taken from each artist's new album. A powerful and explosive cocktail of electronic music genres merging the frozen harsh dark elektro assaults of MILDREDA, the edgy noir dance pop of PSY'AVIAH and the moody EBM/future pop of LLUMEN.


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-- Officials at Microsoft said that independent software vendors would play a key role in the planned fall launch of its Office Small Business Management Edition. "The reason we continue to grow is because of our ISVs," said Mark Young, developer and general manager of ISV strategy at Microsoft, during a day-long ISV forum titled "Opportunity Knocks." "We understand the power of ISVs." To help ISVs promote and integrate with Microsoft's new application, Dave O'Hara, vice president of business development at the technology giant, set out a roster of six resources available for Microsoft ISVs: free product testing, in-the-box promotion, online catalog inclusion, development support, marketing support and customizable marketing templates. Another feature for ISVs is the software development kit, available now, to encourage and assist them in integrating their existing products and creating new ones within the Small Business Accounting software. In addition, the SDK will help them set the language from C# to whatever code they prefer. "The thing I love about SBA," said Young, "is every map is open. Every vertical to horizontal is open and an opportunity." However, one of the maps that remains closed, said Young, was security -- set at base level for heightened security. "The security was built in at a database layer -- far more secure than at any application layer," said Rajat Taneja, general manager of Small Business Applications at Microsoft Business Solutions. Taneja added that customers would find not only advanced security and a brand-new accounting system, but also an enhanced Outlook 2003 integrated with Business Contact Manager. The Outlook with the contact manager would provide a richer sales and marketing experience by offering such tools as a viewable history of tasks for each client, reporting capabilities, and contact information for all those working with or on a specific account.
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You are here: Hare Krishna.ru :: Vaishnava calendar :: 2018–2019
Gaudiya Festival Dates
2018 to 2019 — Sri Gaurabda 533
Please note that this calendar has been prepared according to the directive of Srila Bhakti Sundar Govinda Dev-Goswami Maharaj that Ekadashis and their associated paran times should be calculated according to locality but all other events in the Vaishnava calendar should be observed around the world on the same date that they are observed in India.
Please note that Sri Chaitanya Saraswat Math's calendar for 2019‒2020 will be released just prior to Gaura Purnima 2019.
Calendars for 2018–2019 are available for Almaty, Ankara, Barcelona, Barnaul, Bogotá, Buffalo, Budapest, Caracas, Chelyabinsk, Chiang Mai, Delhi, Dnepropetrovsk, Donetsk, Ekaterinburg, Guadalajara, Habarovsk, Haifa, Hanty-Mansiysk, Harkov, Herson, Honolulu, Johannesburg, Kazan, Kiev, Krasnodar, Krasnoyarsk, Kuala Lumpur, Lima, London, Lugansk, Lvov, Maalot-Tarshiha, Manila, Mérida, Mexico City, Miami, Milan, Minsk, Morelia, Moscow, Nabadwip, New York, Nizhny Novgorod, Novosibirsk, Odessa, Omsk, Orenburg, Perm, Port Luis, Prague, Piter, Quito, Riga, Rome, Rostov-on-Don, Salt Lake City, Samara, San Luis Potosí, São Paulo, Sevastopol, Shenzhen, Simferopol, Smolensk, Sochi, Soquel, Sukhum, Tijuana, Timmins, Tolyatti, Tomsk, Ufa, Uzunja, Vancouver, Velikiy Novgorod, Veracruz, Vinnitsa, Vladivostok, Volgograd, Voronezh, Yaroslavl and Yoshkar-Ola.
If your location is not listed here and you would like a calendar with Ekadashi fasts calculated for your location according to the rules accepted in Sri Chaitanya Saraswat Math, please feel free to contact Sripad Tyagi Maharaj via the web form at gaudiyadarshan.com or Ashutosh Krishna Das via email <email@example.com>.
2003–2017 © Sri Chaitanya Saraswat Math (when copying materials, please publish an active link to harekrishna.ru)


text:
Ronnefeldt Tea-Caddy Milky Oolong
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Before the mid-1970s, special education in our country's public schools was all but non-existent. Many students were either outright denied the opportunity to attend because of their disability, or they received inferior instruction if they were able to enroll.
Too often we hear of terrorist attacks and deadly incidents that in many cases could have been prevented or somehow lessened. Strange and erratic behavior is sometimes the first clue to a potential danger posed to our community. That is why the Kentucky Office of Homeland Security developed the "Eye on Kentucky" program.
Have you ever had a teenager screaming and cursing in your face, throwing things as he stormed through the house? Breaking cabinets? Kicking in doors? Have you ever had to watch a teenager scream and curse at your spouse and you weren't allowed to do anything about it?
It's tough to deal with, let me tell you.
By Sister Claire McGowan, OP
Guest columnist
About a decade ago, Kentucky started to see a welcome trend as the number of highway fatalities began a steady decline. Totals that regularly exceeded 900 a year before 2007 dropped to 638 in 2013, a figure not seen in the commonwealth since the 1940s.
Unfortunately, that was as low as it would go. The number of fatalities on our roads last year was almost a fifth higher than the benchmark set just two years earlier, and through the first seven-plus months of this year, it's eight percent ahead of where it was last August.
There is an unseen enemy attacking Americans today. They hide away in some dingy office in a different country. They are smart. They know exactly what to do and who to target. These enemies are the pirates of our homes, the digital pickpockets who can get your entire fortune if you allow them to dig deep enough. They are scammers.
I don't really know a better word for them. Perhaps: sleaze-buckets? Scum-suckers? Other words I'm not allowed to put into print?
For consistency's sake, we will stick with scammers.
Kentucky received some welcome news last month when a national study found that no state had a smaller gap when comparing the high school graduation rates of students from low- and higher-income families. The average gap across the country stands at 15 percent, but it's just one percent here in the commonwealth. In fact, our low-income students graduate at a higher rate than the overall national average, something only five other states can say.
By Derrick Ramsey
Across Kentucky, many employers continue to battle a shortage of skilled tradespeople combined with the challenges of replenishing an aging workforce. Simultaneously, more and more students are considering the most affordable and efficient path to a high-paying career.
The Girls on the Run program changed Brianna Mattingly's life.
Mattingly, 13, was one of nine girls in Marion County's inaugural class of Girls on the Run at A.C. Glasscock Elementary School in 2011.
At the time, she was a shy nine-year-old who lacked self-confidence.
I remember watching her during our Girls on the Run activities and workouts. I could tell she was special, but it was obvious she didn't believe in herself.
For the last six years, my wife and I have lived relatively in seclusion. In Georgia, we were outsiders – people from the North who didn't know a blessed thing about the South. Never would as far as they were concerned.
Copyright © 2018
The Lebanon Enterprise is your source for local news, sports, events, and information in Marion County and Lebanon, KY, and the surrounding area.


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Americans divided on capital punishment issueBy Adam Dodson | 11/03/2016 1:59pm
Capital punishment has been used by the state of Alabama since the early 1800s. CW / Caroline Japal
Statistically speaking, Americans across the country seem to be less enthusiastic about the death penalty than they used to be. At the height of the 1990s, when a Republican Congress worked with a Democratic president to pass a major crime bill, support for capital punishment was at a record-high 80 percent, according to the Gallup polling company. But almost 20 years later, that number has fallen to around 60 percent, the most recent data from Gallup shows.
Such a statistical shift in public opinion could have an impact in the polls. For the states putting the death penalty on trial, the vote could be much different result in 2016 than it would have in 1996.
This year, voters in California will have the choice between dueling ballot initiatives on the topic of capital punishment. One, California's Proposition 66, will offer Californians the option to speed up executions of those waiting on death row. According to the Los Angeles Times, this proposition is now facing large protest, with those in opposition believing that Proposition 62, which would ban the death penalty altogether, should be passed instead.
While putting the issue to a vote is democratic, experts at the University say it might not be constitutional.
"I have doubts concerning its constitutionality for a few reasons, in cases dealing with the means of execution, the Court has clarified what is and is not constitutional," UA constitutional law professor Allen Linken said. "Pragmatically, it places burdens on trial courts that may not be feasible."
Even where the death penalty is still in full force, numbers show that the rate at which people are being executed has slowed down.
According to The Texas Tribune, this year, Texas will execute its lowest number of people in 20 years. Seven people have faced execution in 2016, with only one more scheduled. This decline in executions is in part due to more appellate judges rescheduling or stopping executions, which has happened 15 times this year alone, the Tribune reported.
But not all of the change has been democratic. Some death penalty roll-back has come from state judges issuing rulings from the bench.
In August, the Delaware Supreme Court struck down its state's death penalty statute, claiming that the sentencing procedures were unconstitutional. Around the same time, the Nebraska legislature voted to repeal the death penalty and override a gubernatorial veto of the bill.
But what about Alabama? The question still remains as to whether or not the Yellowhammer State's policy will see any changes in the near future – let alone a statewide vote. A historical defender of capital punishment, Alabama has executed 53 people since the temporary ban on the death penalty in the U.S. ended in 1976. In that same time only five states – Texas, Virginia, Florida, Missouri and Oklahoma – have executed more.
While the issue is not on any ballots in Alabama, several UA campus voices weighed in on how the state might deal with the issue in the future.
"The opposition to the death penalty has already made its way here," said Josh Shumate, a graduate student and vice president of UA Young Americans for Liberty. "It just takes a while [to see a difference] in conservative states like Alabama."
Even if Alabama voters did democratically uphold the death penalty, the practice still faces many key constitutional questions. There is a debate of whether the practice itself is constitutional under the Eighth Amendment, which prohibits cruel and unusual punishment, and whether the states or federal government should be in charge of setting the standards.
Civil libertarians and liberals have raised due process concerns surrounding capital punishment and especially with the speeding up of executions. According to Amnesty International, over 150 people have been released from death row after wrongful convictions. This includes Daniel Wade Moore, an Alabamian, who served seven years on death row until 256 pages of withheld evidence were released that proved his innocence.
Similarly, Alabamian Anthony Ray Hinton was wrongfully sentenced to death row, but his story had a happier ending. According to AL.com, Hinton spent 30 years in prison for two murders, but he was ultimately exonerated in April 2015.
Alabama is also the only state where judges frequently override a jury's decision to not sentence someone to death.
"I believe the death penalty is constitutional and should be controlled by the states," Shumate said. "However, in my opinion it gets bad with some states like Alabama who overuse it."
Lobbying efforts to repeal the death penalty in Alabama are run largely by Project Hope to Abolish the Death Penalty, which focuses on educating Alabama citizens on the problems surrounding death penalty convictions.
But those opposed to the current iteration of the death penalty offer differing solutions. Some advocate for the compete abolition of the practice, while others simply wish to reform the system. Many state governments that have recently repealed capital punishment have proposed that all death row inmates have their sentences changed to life without parole. Proponents of abolishing the death penalty point to how expensive it is for the state to execute someone and how much better that money could possibly be spent elsewhere.
To many, the death penalty would not be problematic if the system was implemented correctly. Many believe that a sizable portion of the pro-death penalty ideals will fade away over time, a "generational" issue.
"I believe the older generation follows the 'eye for an eye' mentality, while the younger generation tends to be more progressive-minded," said Andrew Capecci, a senior majoring in finance. "To me, it is an ethical conflict whether to spare a man's life based on the verdict of 12 random citizens."
But experts say that Alabama's conservative majority does not appear to be apt to vote away the death penalty any time soon.
"I have a tough time foreseeing Alabama lawmakers removing the death penalty from the books, even if there is dwindling support," Linken said. "What may affect it most would be executive action by the Governor or the Supreme Court ruling it is systematically broken and declaring it is unconstitutional."
Daniel Ashford, a senior majoring in finance and treasurer for the University's Young Conservatives, echoed the position held by many in the Alabama electorate. Ashford is in favor of the death penalty, and offered rationale explaining why he does not believe it conflicts with his Christian beliefs.
"I support death penalty because it upholds justice for murder," Ashford said. "It does not go against my Christian beliefs because of Romans 13:4, which states that the government must execute judgement by the sword. The 'sword' isn't just symbolic for justice, but also for death through justice."
The belief that the death penalty may eventually die out in Alabama is at the very least one that will not be decided by voters until the future. But elsewhere, Americans will face a decision to make on their ballots this November that will shape the direction of the conversation going forward.
Please note All comments are eligible for publication in The Crimson White.


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Putting drunk driving to the test
The standard sobriety tests that are given to suspected drunk drivers by police across the country originated with a small Los Angeles organization called the Southern California Research Institute.
In the photo above, which ran in the Los Angeles Times on March 20, 1977, a research assistant sits at the wheel of a driving simulator that was used by the Southern California Research Institute to test reactions to drugs and alcohol. The photo was taken by Times photographer John Malmis.
The institute was the brainchild of Herbert Moskowitz, an experimental psychologist who led pioneering research on the effects of alcohol and drugs. The institute's work helped produce standardized field sobriety tests and pushed policymakers to set lower legal limits for intoxicated driving.
Moskowitz devised rigorous experiments, including the early use of driving simulators, that demonstrated drivers' growing impairment as they consumed increasing amounts of alcohol. His research found that even a single drink, a much smaller amount than previously believed, could significantly slow the brain and raise drivers' risk of a crash.
The Southern California Research Institute continued to produce leading research on drunken, drugged and drowsy driving, as well as intoxicated boating, into the 21st century. The organization closed after Moskowitz died in 2012.
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cervezas ('survey says')
For lack of more and just because and well, it's ready-made, I present to you, dear reader: another blog questionnaire. Tag, you're it!
And Today's Music Rec is, in no particular order, the following Go-Go's songs, singled out for Kathy Valentine's frickin lickable bass lines: "Turn To You"; "Head Over Heels"; "Vacation"; "We Got The Beat"; "Our Lips Are Sealed" and "This Town". Thank you, Ms. Valentine for your work, for you are, as my friend Wynona says, one of my musical 'she-roes'
And I want some props to how sad it is that I read Kafka and then the Communist Manifesto today at my cafe du saison FOR FUN, as diversion from my exams and teaching--yes, it's true, getting a head start on a civ. course I'm helping teach in the fall and Lawd KNOWS I won't get to it between now and Labor Day. Workers (and Geeks) of the world, unite.
Ah, good old Franzie K. The Czech who was...not really very Czech, now was he? German as a minority language indexing his Jewish heritage versus Czech as a marker of Bohemian nationalism of the time: discuss!
OK, on to the survey. I must preface it with a statement on how quite high-schoolish it seems to me, since going back only three years really aint that much these days, honey.
3 YEARS AGO TODAY (21 July 2003)
How old were you?:
three years younger. 32. Shit fire.
Where did you go to school?
The State Penn
Where did you work?:
Third floor, the "B" building, done with my first year of the PhD, back when I thought it would really take 'only' four years. Boy was I dumb.
Where did you live?:
Club 164
How was your hair style?
Blonde, same as it ever was.
Did you wear glasses?:
Who was your best friend?:
Who was your boyfriend/girlfriend:
the guy who was no longer really my boyfriend and it sucked big time.
Who was your celebrity crush?:
Special Agent Fox Mulder (damn that beyotch Scully who had fabulous clothes, a medical degree, AND got to be all 'are they or aren't they' with Muldo!)
Who was your regular-person crush?:
the guy who was the first real distraction since the one who was no more.
How many tattoos did you have?:
How many piercings did you have?:
What car did you drive?
The 1985 Buick Century.
What was your favorite band/group?:
Hm, what was I into three years ago, which guitars was I on? Dixie Chicks?
What was your worst fear?:
Not recovering from a neck injury
Had you smoked a cigarette yet?:
Had you gotten drunk or high yet?:
Had you been to a real party yet?:
What, there are fake parties?
What was your main goal?:
To stew in grad school for a spell?
Had your heart broken?:
Had broken someones heart?:
HA HA HA!!! LETS SEE WHAT YOU ARE NOW !!!!! (21 July 2006)
How old are you?:
Three years older than the above. Doy!
What grade are you in?
Where do you go to school?
Still at PSU
Where do you work?:
Still performing jedi mind tricks in the cubes in the "B" bldg., among other places
Where do you live?:
Still Club 164
Where do you hang out?:
Saints (good coffee), Chumles (good gin tonics), The Corner Room (burgers, enough said), Websters (smelly but for those days when I crave sketchy faux alternative types, it's fab) Herwigs (meat!), home, etc.
Do you have braces?:
Do you wear glasses?:
No, but I'm going to get an eye exam soon since I have vision insurane.
Still talk to any of your old friends?:
Who is your celebrity crush?:
Keith Urban; ficticious tennis star Dana Fairbanks; Zinedine Zidane.
How many tattoos do you now have?:
How many piercings have you had?:
What kind of car do you have?
The 1985 Buick, still only 44K original miles, thank you very much.
What is your favorite singer/group?:
my collection is vast but off the top of my head: Amy Grant, Dolly Parton, Annie Lennox, Terri Clark, Dixie Chicks, Bruce Springsteen, Ella Fitzgerald, Diana Krall, so many....
What is your biggest fear?:
breast cancer; redux of pain from said neck injury
Have you smoked a cigarette yet?:
yes, now stop asking, it's a terrible thing to do. Regularly.
Have you been to a real party?
Honey, I AM the real party
What's your main goal:
Get enough sleep and exercise
Has your heart been broken?:
What since the last time? On smaller scales.
Have you broken someones heart?:
Not intentionally!
69 Random Questions
1) Do you have a penis?
No, nor do I have 'balls'
2) Do you pray?
3) Are you in love?
4) Ever wish on stars?
I think so
5) Do you believe in karma.
6) What's your zodiac sign?
7) Have you ever almost died?
Probably (SEE: 'le petit mort')
8) Ever broken any bones?
9) Do you cry during sad movies?
all the time, I'm such a sap that way, I am not afraid to admit iit.
10) Do you like to dance?
11) Ever laid under the stars?
why did I want to insert 'gotten' there? yes, stars, yes, I'm all about open sky
12) Ever sat on a rooftop?
yes, have you?
13) Is there such thing as a soul mate?
14) Could you live without the television?
short term only
15) Could you live without music?
16) Do you have any self-inflicted scars?
17) What do you dislike the most about life?
that post-modern and/or retro-futuristic thinking has prompted analysis of EVERYTHING. Some days I'd rather be a peasant delivering babies in the mud, not knowing that I can even think about things like whether or not I am happy, etc.
18) Have you ever been to jail?
19) Ever had a job for less than a day?
20) Ever been fired on your first day?
21) Ever been fired because of your attitude?
no, but I did have to write an apology note to our 8th grade choir teacher at my Catholic girls' middle school because I was 'being fresh' and all coppin' a 'tude with her.
22) Do you get jealous of other people?
I'd say more 'envious' rather than jealous
23) Would you rather love someone or be loved?
I'd rather have the two inherently linked.
24) What's under your bed right now?
I'm happy to say not much because I vacuumed under there after MONTHS.
25) Ever done anything illegal?
26) Ever dumped somebody?
27) How cool are you?
Cool enough to feel like a total DORK answering these ass questions.
28) Do you support abortion?
I support the choice to get one or not.
29) Do you believe in God?
30) Did you graduate high school?
31) Do you wear the same clothes two days in a row?
yes if I feel like it
32) Have you ever driven someone crazy?
no, uh, yes
33) Ever bullied someone?
hahah! I am the oldest sister/first child, so, clearly-yes.
34) Ever done the Macarena?
yes (sigh, just got flashbacks of several summer camps working in the Austrian Alps, macarana-ing in high-altitude diskotheques)
35) Do you act your age?
yes, altough I have never seen any sort of "Guidelines of How To Conduct Oneself at Age 35". Weird, this is question #35...
36) Is it okay to disrespect your parents?
no, and it's not ok for them to disrespect you
37) Do you flush the toilet when you're done?
"If it's yellow, let it mellow / if it's brown, flush it down". Water conservation benefits us all!
38) How long do you stay in the shower?
it totally depends on what I'm doing there
39) What kind of soap do you use?
I have an array, depending on skin moisture level, barometric pressure, etc. It's what keeps me doing #35.
40) Are mullets cool?
41) Spiderman, Batman, or Superman?
none; James Bond
42) Do you like your middle name?
I have the best one in the world
43) whats your favorite color?
44) Has anyone ever cheated on you?
I have had my suspicions
47) Favorite flower?
48) Have you ever shaved your head?
49) Do you think marijuana should be legal for medicinal use?
50) Do you think it is okay to drink and drive?
51) If you won $1 million dollars, what would you buy first?
52) Do you fear terrorism?
no, I tend not to fear concepts
54) What's your favorite candle scent?
mandarin orange around Christmastime
55) Do you use profanity?
56) Who's the last person you talked to on AIM?
57) What's something you're ashamed of?
58) What woke you up last night?
the humidity
59) What did you dream about last night?
Swimming and breasts; and that an old friend was twice as tall as me. WTF???
60) Ever been to the zoo?
61) How many beers did you have today?
62) What's the last movie watched?
"Der Junge Törless" and I'm currently viewing the dramatic 80's TV mini series "The Thorn Birds"
63) Are you usually late or on time?
a tad late
64) What's a cartoon you watch?
none, but as a kid I liked the Smurfs for the storylines
65) Do you have any imaginary friends?
not that I know of
66) Are you waiting on something right now?
yes, something to sell on Ebay.
68) Who's ugly?
GWB when he opens his mouth on TV
69) Are you worried about something?


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View our Final Report and Program Evaluation for 2016-17.
Serving 930 students from Rosa Parks Elementary and Wilson Middle School this year,
School in the Park (SITP) once again holds fast to Sol Price's program vision of
building student character, confidence, competence and curiosity. Museum educators
from nine Balboa Park institutions, including the San Diego Zoo, provided a collective
total of 38 curricular units during the 2016-17 academic year. read more ….
View final reports for the last five years below:
- External Report:SITP/USC: 2015
- End of the Year Report: 2015-16
- End of the Year Report: 2014-15
- End of the Year Report: 2013-14
- End of the Year Report: 2011- 12
- Evaluating the Academic & Behavioral Impact of SITP: 2015
Preview our external evaluation done by Vital Research in 2014-15:


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The Magazine for Underwater Professionals
Jul/Aug 2015
Michael Cocks returns to the Divers Institute of Technology, and finds the school has its sights set on becoming the world leader in ROV training
In March I paid a welcome return to the Divers Institute of Technology (DIT) in Seattle, USA, my fifth visit since 2001. The school is run by Bruce Banks, a former Commanding Officer of the United States Navy Diving and Training College. Since my last visit more than three years ago, much progress has made, with many more new projects provided for the students, the offering of a Divers Medical Technician (DMT) course compliant with IMCA, and a decision to begin intensive ROV training.
In the past I have raised two slight niggles; namely the lack of a wet bell and the scuba training occurring towards the end of the 28-week course. The first issue is being resolved, with a wet bell to be installed on the excellent Response vessel. As much as I am against teaching scuba in a surface-supplied training course, DIT continues to provide NAUI (National Association of Underwater Instructors) scuba because scuba certification is required by its international surface-supplied diving standard. I believe there is certainly a place for a professional scuba course for media and scientific divers, but to my mind scuba has no place in commercial diving work; I also believe the large majority of diving deaths occur in scuba.
I started off my two-day visit in the company of Bill McGilton, who had looked after me on my last visit. Bill previously spent 36 years at Boeing and helped in the American space programme. I was pleased to learn that, at an age slightly older than me, Bill is still diving and is also making considerable progress in developing a substance to rapidly increase the growth of coral in the Philippines, with the aim of raising the fish population there.
Bill introduced me to Eric Compton, a new arrival, who has been working with Bill to produce a 24-week ROV course. Eric's career started in the US Navy as a sonar technician on nuclear fast attack submarines. Eric has 35 years of ROV experience, having worked with Oceaneering, Global Diving and Salvage and Honeywell, where he led the manufacture, integration and testing of the US Navy's SLQ-48 Mine Neutralisation Vehicles.
DIT's 24-week ROV course, to start later in 2015, will be to IMCA and Diver Certification Board of Canada standards, and DIT hopes to become the leading ROV training school in the world. The course comprises two 12-week courses; the first 12 weeks provide the students with aptitude but no experience; the students are given the prerequisite knowledge in basic maths, electronics, hydraulics and mechanics to allow them to qualify for the second ROV technician and pilot 12-week course. Because this course will offer government and VA (Veterans Administration) loans and grants, this ambitious course is an affordable means of training a new generation of ROV technicians and pilots.
On the diving front I was shown a number of new underwater projects for the students to work on. The course is still as intensive as ever, but apart from the last deep-diving session, training now takes place on the first four days of the week. Well over half of the students come from those who have served in the armed forces, who get help with their fees. As required by the government, in order to obtain funding, more than 80% of the students find work after graduation. I spent my second day with students practising deep diving and the use of the decompression chamber on the Response, under the sharp eyes of Mike Kleinfelder, who has been at the school for eight years, and Doug Irish, newly arrived after extensive dive work in the US Navy. The students had a further two and a half weeks of training to go.
One recent addition – very welcome to the students – is to have one dive in the old Mark V equipment; on a previous visit I had dived in the equipment used by Robert de Niro in the film Men of Honor. They can also undertake a short extra course on helmet maintenance.
The school seems in very good shape and this is confirmed by a recent article in the Underwater magazine of the American Association of Diving Contractors. The students have to work closely together, both out and under the water, and most seemed to have done the necessary research before choosing to come to the school. As in the past, I was well looked after by Bruce Banks and I look forward to returning, when the wet bell and ROV courses are up and running. DIT maintains a close link with the Underwater Centre in Fort William, UK, and many of the students go on to do the saturation course there or in Australia.
Jul/Aug 2018


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|Message view
|« Date » · « Thread »
|« Date » · « Thread »
|"Hairong Kuang (JIRA)" <j...@apache.org>
|[jira] Commented: (HDFS-1509) Resync discarded directories in fs.name.dir during saveNamespace command
|Thu, 16 Dec 2010 08:01:03 GMT
[ https://issues.apache.org/jira/browse/HDFS-1509?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12971992#action_12971992 ] Hairong Kuang commented on HDFS-1509: ------------------------------------- I agree with Eli that this looks good except for a couple of improvements: 1. Could restore the accidentally commented-out tests? 2. attemptRestoreRemovedStorage formats the newly added previously removed storage directories, which calls saveCurrent that save fsimage to disk. Later on saveNamespace save the namespace again. Could you make name space saving to be done only once? > Resync discarded directories in fs.name.dir during saveNamespace command > ------------------------------------------------------------------------ > > Key: HDFS-1509 > URL: https://issues.apache.org/jira/browse/HDFS-1509 > Project: Hadoop HDFS > Issue Type: Improvement > Components: name-node > Reporter: dhruba borthakur > Assignee: dhruba borthakur > Attachments: resyncBadNameDir1.txt, resyncBadNameDir2.txt > > > In the current implementation, if the Namenode encounters an error while writing to a fs.name.dir directory it stops writing new edits to that directory. My proposal is to make the namenode write the fsimage to all configured directories in fs.name.dir, and from then on, continue writing fsedits to all configured directories. -- This message is automatically generated by JIRA. - You can reply to this email to add a comment to the issue online.
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Courthouse on the Square – Denton County, TX
Harweldon Mansion
Harweldon interior door
The Pioneer Woman's Mercantile – Pawhuska, Ok
Pawhuska Ok Interesting and sketchy!
Pawhuska OK
Courthouse on the Square – Denton County, TX
Harweldon Mansion
Harweldon interior door
The Pioneer Woman's Mercantile – Pawhuska, Ok
Pawhuska Ok Interesting and sketchy!
Pawhuska OK
Monday was a holiday for me and I refuse to sit in the house this time of year! It was abnormally warm at 87° here in Oklahoma. I was hoping to drive south a couple hours to the Ouchita National Forest by the Arkansas border and see the changing leaves on the Talimena National Scenic Byway but I am a couple weeks too early. So my dad told me to check out Cedar Lake down in the valley outside of Talihina.
A small 78 acre lake in a beautiful valley, it is the home of the Oklahoma State Record Largemouth Bass at 14lbs 14oz… I was hoping to find someone to ride shotgun on my road trip, so I wouldn't have to go solo. Low and behold my oldest son who just so happens to be on a college fishing team, had finished his classes early and said come pick me up. I was ecstatic, to spend the day fishing with him!
These stairs caught my interest, love the feeling of this photo. I was very anxious to get my fist look at the lake!
Doubled up on this cast, love catching these little bass with my new ultra light spin cast with 4lb line. It's a fight every time!
The smell of pine was so strong and lovely!
Gorgeous end to a great day!
Got to make the trek home through a big storm that popped up unexpectedly, but overall a beautiful adventure making wonderful memories with my son. Priceless!
Thanks for reading!
This is My Happy Place, this is where a part of my heart will always be.
My kids ran, played, explored, fished and hunted on this 47 acres on Lake Hudson for eleven years, Two of them came straight from the hospital to call this home.
They learned so much about life and life lessons from the great outdoors here and acquired a love for nature.
This is Spavinaw Creek, the town of Spavinaw Oklahoma is a short drive and is the Birthplace of Mickey Mantle.
Following the Trail of Tears (1839) Eastern Cherokees began arriving in the area. Before the lake was made, they say along the original creek bed that runs next to these bluffs was an Indian Village.
When they would let the water down to make repairs we would find Arrowheads and various artifacts left behind by the Native Americans.
I've always found this area to be very beautiful & peaceful, I call it my little piece of heaven.
I have a waterfront subdivision that I developed when I was thirty and named it for the Hollow that runs through it. Solemn Hollow Such an appropriate name!
Also I still have a waterfront lot and hope to live there again someday in hopes my kids and future grandchildren can enjoy it and make new memories.
Thanks for reading!
Happy Friday!!
Traveling, discovering and seeing new places is one of my favorite things to do, I travel as much as my job allows, which means a lot of short trips close to home and an occasional longer journey to a new place I've yet to explore.
I love big cities, their museums, history and different cultures but I am mostly drawn to nature and the beauty of God's handiwork.
I have purchased a National Park Passport and I am anxious to visit as many as I can along with some of the state parks in my area.
I find myself taking a lot of photos so I will never forget the places I've been and seen. Recently I've been thinking that a travel blog would be a great way to document my adventures although I've never blogged before, this will just be one more adventure I will try my hand at and embark on.